Submission date: 24 June 2020

Abstract:

We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of dimension of a set definable in the structures including the addition property, which is the dimension equality for definable maps whose fibers are equi-dimensional. A decomposition theorem into special submanifolds is also demonstrated.

Mathematics Subject Classification: 03C64

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Full text arXiv 2006.13481: pdf, ps.